Final answer:
The collapse of the Abbasid Caliphate was a significant sociopolitical change resulting from the Mongol invasion. Despite the end of the Abbasid rule, Islam's influence persisted and even expanded, with the Il-Khanate embracing Islamic culture and civilization.
Step-by-step explanation:
The sociopolitical changes that resulted from the events described in the passage include the collapse of the Abbasid Caliphate. The Mongol invasion under a grandson of Genghis Khan in 1258 ended the Abbasid rule, which marked a profound change in the region's political landscape. However, Islam continued to exert a significant influence; rather than diminishing, it expanded with the rise of the Ottoman Empire and the Safavids. The passage also notes a change in the fourteenth century as the Il-Khanate, part of the Mongol Empire, embraced Islamic culture and civilization following the conversion of ruler Ghazan to Islam. This indicates a continuation and integration of Islam rather than an end to its influence or the introduction of Buddhism into Persia. Moreover, while the Mongol Empire did exact tributes from its conquests, the passage does not detail the establishment of a Mongolian tribute empire as a new system but refers to the expansion and influence of existing entities such as the Ottoman and Safavid Empires.